Statements (105)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:Polygon |
| gptkbp:definedIn |
the convex hull of a finite set of points in Euclidean space
|
| gptkbp:describes |
half-space representation
vertex representation |
| gptkbp:dimensions |
n-dimensional
|
| gptkbp:example |
gptkb:cross-polytope
cube simplex hypercube regular polytope |
| gptkbp:has_face |
gptkb:mountain
edge vertex Cell facet |
| gptkbp:hasApplication |
gptkb:geometry
gptkb:machine_learning biology chemistry combinatorial optimization computer science data analysis economics game theory operations research physics mathematical modeling linear programming |
| gptkbp:hasDual |
gptkb:dual_polytope
|
| gptkbp:hasProperty |
convex
combinatorial structure bounded can be orientable can be 0-1 polytope can be Archimedean polytope can be Archimedean solid can be Birkhoff polytope can be Catalan polytope can be Johnson polytope can be Platonic solid can be antiprism can be associahedron can be bipyramid can be centrally symmetric can be chain polytope can be chiral can be cyclic can be decomposed into simplices can be edge-transitive can be equiangular can be equilateral can be face-transitive can be facet-transitive can be integral polytope can be isotropic can be lattice polytope can be neighborly can be non-orientable can be order polytope can be permutohedron can be prism can be pyramid can be rational polytope can be regular or irregular can be regular polytope can be regular-faced can be semi-regular can be simple or simplicial can be simple polytope can be simplicial polytope can be snub polytope can be stellated polytope can be transportation polytope can be triangulated can be truncated polytope can be uniform polytope can be uniform-faced can be vertex-transitive can be zonotope every face is a convex polytope faces are themselves convex polytopes finite number of edges finite number of extreme points finite number of faces finite number of facets finite number of vertices |
| https://www.w3.org/2000/01/rdf-schema#label |
Convex polytope
|
| gptkbp:important_theorem |
gptkb:Euler's_formula
gptkb:Minkowski–Weyl_theorem McMullen's conditions Upper bound theorem |
| gptkbp:relatedConcept |
gptkb:Polygon
gptkb:simple_polytope gptkb:simplicial_polytope convex hull face lattice |
| gptkbp:represents |
intersection of a finite number of half-spaces
|
| gptkbp:studiedBy |
gptkb:geometry
combinatorics optimization |
| gptkbp:subclassOf |
gptkb:Polygon
gptkb:Convex_set |
| gptkbp:bfsParent |
gptkb:Polygon
|
| gptkbp:bfsLayer |
5
|